The invention is based on a fuel injection pump for internal combustion engines. In a fuel injection pump of this kind, known from German Offenlegungsschrift 25 03 355, upon the closure of an intake bore with the aid of a magnetic valve, fuel can flow out of a suction chamber into a work chamber via a diversion cross section at a quantity adjusting device and via a relief conduit in the pump piston, so that despite a closure of the intake bore, fuel can still proceed to injection. If the pressure in the interior of the suction chamber is sufficiently high, and if the diversion cross sections for the rapid relief of the pump work chamber are sufficiently large, then the quantity of fuel aspirated via this route suffices to prevent the internal combustion engine operated with this fuel injection pump from shutting down. As a result, the intended purpose of shutting down the engine by the magnetic valve in the intake bore fails to be attained.